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Multiscale modeling of glioma invasion: from receptor binding to flux-limited macroscopic PDEs

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Anne Dietrich, Niklas Kolbe, Nikolaos Sfakianakis, Christina Surulescu

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Abstract

We propose a novel approach to modeling cell migration in an anisotropic environment with biochemical heterogeneity and interspecies interactions, using as a paradigm glioma invasion in brain tissue under the influence of hypoxia-triggered angiogenesis. The multiscale procedure links single-cell and mesoscopic dynamics with population level behavior, leading on the macroscopic scale to flux-limited glioma diffusion and multiple taxis. We verify the non-negativity of regular solutions (provided they exist) to the obtained macroscopic PDE-ODE system and perform numerical simulations to illustrate the solution behavior under several scenarios.
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Original languageEnglish
JournalArXiv e-prints
Publication statusPublished - 7 Oct 2020

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